Nigeria's military has been involved in heavy fighting with Islamist insurgents armed with sophisticated weapons from Libya as it steps up an offensive aimed at flushing out Boko Haram from its north-eastern bases.

"They have been putting up fierce resistance and they are very, very well-armed with weapons from Libya," a senior military official told the Guardian, adding that most of the militants who have waged a bloody four-year battle to create an Islamist state have scattered across the region's semi-desert borders.

A renewed military campaign, including aerial bombardments of Boko Haram training camps in three remote states which were put under emergency rule this month, has led to the capture of almost 200 militants and the death of dozens in a week, according to the military. In one raid, a helicopter gunship was hit by anti-aircraft and anti-tank fire, a military source said.

In a sign of increasing concerns about jihadist movements jumping borders, Nigeria has also asked neighbouring Niger for military support as it seeks to police 870 miles of shared desert borders. With phone lines cut off across most of the three north-eastern states as advancing soldiers try to prevent militants from warning of approaching raids, residents fleeing across porous borders also risks destabilising a region already reeling from a separate Islamist insurgency in Mali.

"It's only by the goodwill of soldiers and by virtue of my position I was able to leave the city. All the entry points to and from [Borno state capital] Maiduguri are blocked by the military but they let me through," said Suleiman, a civil servant who quit the city at the epicentre of the insurgency with his family of four. Outside the city walls, he said, trucks carrying food and market produce were lined up awaiting entrance.

"We have been used to seeing soldiers and checkpoints for the past two years in Maiduguri, but it is having a real impact on the economic activity," he added.

In Maiduguri, where militants are deeply enmeshed in the population, soldiers carrying out house-to-house searches after placing a 24-hour curfew in some neighbourhoods discovered stockpiles of weapons including rocket-propelled grenades, a defence spokesperson said.

"Life has still not returned to normal in these areas, shops aren't open. People are just sitting at home scared and sweating," said Amina, a secretary in the 202 neighbourhood. "They arrested a lot of people here in operations in the night."

Nigeria's military, already assisting a west African-led force in Mali, has asked for help from Niger. "We currently have military operations under way in Nigeria in three federal states to combat terrorism and we would like to have Niger's support in the common fight against these terrorists," said Nurudeen Muhammed, Nigeria's minister of state for foreign affairs. He did not specify what kind of military co-operation that might mean.

Fighting in border areas has prompted a wave of refugees into landlocked Niger, ranked the world's least developed country. "We have already had a huge flood of refugees from Mali, which has had an impact on food security," said Artur Mallam of Save the Children in the Nigerian capital, Niamey, who estimated at least 500 Nigerians had settled in frontier towns in five days.

The tough stance against Boko Haram has proved largely popular so far, with many seeing it as a welcome acknowledgement of the disintegrating security situation in parts of the north. Nigeria has previously used military means to quell religious uprisings, including one in the north's main city of Kano that left some 5,000 dead in the 1980s.

"Our people have no problem with the soldiers coming here as long as they follow the rule of the law," said Ahmad Sabo, a village elder in Borno.

The Nigerian military said it would release all female Boko Haram suspects to help peace efforts.

A spokesperson said: "The measure, which is in line with presidential magnanimity to enhance peace efforts in the country, will result in freedom for suspects including all women in custody."